The Surly Disc Trucker (DT) is heavier than the Long Haul Trucker (LHT), whether you're considering the frame, fork, frameset or complete bike built from same components.

From 2011 Surly catalog, page 6:

for 58cm LHT frame, weight = 2,340g ; for 700c fork with 300mm steerer, weight = 1,020g

total = 3360g for a 58cm LHT frameset

These figures were published for years, possibly from the first LHT back in ~2004. The earliest page I can locate with the "Wayback Machine" is from 9.27.2009 (click on frame highlights tab, then look near bottom of page). Surly appears to have stopped publishing this info after 2011 on both LHT web page and annual catalog.

Surly also published the weight of the DT frame and fork when it debuted in 2012: weight for a 58cm frameset and 700c fork with 300mm steerer:

for 58cm DT frame, weight = 2,580g ; for 700c fork with 300mm steerer, weight = 1,130g

total = 3710g for a 58cm DT frameset

According to Surly, a 58cm DT frameset weighs 350g (10%) more than a LHT frameset. Note both frame and fork of the DT are heavier than those of the LHT.

I own a 56cm 2012 DT, which I weighed when it was new, before building into a complete bike. The frame weighed 2,474g and the 700c fork with 300mm steerer weighed 1,186g, for a total frameset weight of 3,660g. This corroborates Surly's published weight of 3,710g for a 58cm DT frameset.

LHTs are equipped with Tektro CR720 cantilever brakesets weighing ~160g each. DTs are equipped with Avid BB7 disc brakesets weighing ~335g each. The DT requires an additional ~90 cm of brake cable and ~140 cm of housing over a LHT, which adds another 70g weight. So that's 2*(335-160)+70=420g extra weight for a DT for the brakes and cables.

Frameset weight difference (350g) plus brake weight difference (420g) means a 58cm DT will weigh 770g / 1.7lbs more than a LHT built with all the same parts, excepting brakesets, cables and housing.

This largely explains why my old LHT weighed ~28 lbs, and my DT built from the same components (excluding brakes, tires, wheels and fenders) weighed ~30 lbs.

Back to the original topic. IMO, rim brakes of the LHT are adequate if you ride on pavement in mostly dry conditions. Rain and mud conditions, and/or use as a commuter in traffic probably justifies the ~2 lb weight increase for disc brakes. Another option is to convert the front only of a rim-braked bike to disc brake, which would yield most of the braking of an all-disc-brake bike with only half the weight penalty (a DT fork is perfectly compatible with a LHT frame).